A new computational technique is proposed for predicting the state of lowest energy for proteins. The new method, called the homotopy method, creates a mapping of low energy states between two sequences of amino acids and follows this mapping from the state of lowest energy of one sequence to the lowest state of energy of the other. The goal of this research is to implement the homotopy method for use with data from the Protein Data Bank (PDB) so as to map the lowest energy state of proteins with known tertiary structure to the lowest energy state of proteins with unknown tertiary structure. The prediction of tertiary structure from the amino acid sequence of a protein has proven to be a computationally intractable problem in contemporary computing environments even for modest size proteins. The homotopy method has been applied successfully to problems in other areas of science and mathematics to overcome several of the major setbacks, which lead to this computational intractability for predicting protein structure. Preliminary results of using the homotopy method to predict the tertiary structure of chains of charged particles using simple potential energy functions show promise that this method can outperform the current state-of-the-art computational techniques in terms of accuracy and improving the likelihood of predicting the structure with lowest energy.